Antiderivative Formulas

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Last updated 4:42 AM on 4/16/26
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13 Terms

1
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∫xn dx\int x^{n}\,dx

xn+1n+1+C\frac{x^{n+1}}{n+1}+C

2
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∫1x dx\int\frac{1}{x}\,dx

ln⁡x+C\ln x+C

3
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∫ex dx\int e^{x}\,dx

ex+Ce^{x}+C

4
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∫bx dx\int b^{x}\,dx

bxln⁡b+C\frac{b^{x}}{\ln b}+C

5
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∫sin⁡x dx\int\sin x\,dx

−cos⁡x+C-\cos x+C

6
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∫cos⁡x dx\int\cos x\,dx

sin⁡x+C\sin x+C

7
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∫sec⁡2x dx\int\sec^2x\,dx

tan⁡x+C\tan x+C

8
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∫csc⁡2x dx\int\csc^2x\,dx

−cot⁡x+C-\cot x+C

9
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∫sec⁡xtan⁡x dx\int\sec x\tan x\,dx

sec⁡x+C\sec x+C

10
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∫csc⁡xcot⁡x dx\int\csc x\cot x\,dx

−csc⁡x+C-\csc x+C

11
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∫11−x2 dx\int\frac{1}{\sqrt{1-x^2}}\,dx

sin⁡−1x+C\sin^{-1}x+C

12
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∫11+x2 dx\int\frac{1}{1+x^2}\,dx

tan⁡−1x+C\tan^{-1}x+C

13
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∫1xx2−1 dx\int\frac{1}{x\sqrt{x^2-1}}\,dx

sec⁡−1∣x∣+C\sec^{-1}|x|+C